Question: Solve for $x$ and $y$ using elimination. ${5x+3y = 77}$ ${-6x-3y = -87}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $3y$ and $-3y$ cancel out. $-x = -10$ $\dfrac{-x}{{-1}} = \dfrac{-10}{{-1}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {5x+3y = 77}\thinspace$ to find $y$ ${5}{(10)}{ + 3y = 77}$ $50+3y = 77$ $50{-50} + 3y = 77{-50}$ $3y = 27$ $\dfrac{3y}{{3}} = \dfrac{27}{{3}}$ ${y = 9}$ You can also plug ${x = 10}$ into $\thinspace {-6x-3y = -87}\thinspace$ and get the same answer for $y$ : ${-6}{(10)}{ - 3y = -87}$ ${y = 9}$